Without getting into Civil Rights Acts and such, it's simply that gun owners/carriers are not part of what's considered to be a protected class. Carrying a gun isn't a race, gender, or religion. It's a behavior. Prohibiting us isn't discrimination any more than a "No Shoes No Shirt" sign.
It stinks, we all hate it, but, it's really best. Think about it, do we REALLY want government MAKING a business allow certain behaviors on their own property? THAT'S an awfully slippery slope. You can't allow big government to begin forcing private business owners to allow guns without opening the door to big government FORCING you to allow a Jehovah's Witness into your home....after all, THEIR freedom of religion, expression, and speech is equally protected by our constitution. We cannot just pick and choose which parts of "big government" are convenient for us.
The constitution governs government anyway. It has no authority over private property or business in this regard, and, rightfully so, in as much as it blows at the same time.
Keeping our government small also, by the way, goes a long way to protecting your right to NOT go into that business FWIW.
We hold freedom to a very high regard, and, we regularly lament losses of freedoms around here. Why would you WANT the government to trample on any?